Semigroups in Complete Lattices
Quantales, Modules and Related Topics
(Sprache: Englisch)
This monograph provides a modern introduction to the theory of quantales.
First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to...
First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to...
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Klappentext zu „Semigroups in Complete Lattices “
This monograph provides a modern introduction to the theory of quantales.First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research.
This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.
Inhaltsverzeichnis zu „Semigroups in Complete Lattices “
Introduction.- 1 Foundations.- 2 Fundamentals of Quantales.- 3 Module Theory in Sup.- Appendix.- References.- Index.
Autoren-Porträt von Patrik Eklund, Javier Gutierrez Garcia, Ulrich Höhle, Jari Kortelainen
Patrik Eklund develops applications based on many-valued representation of information. Information typically resides in the form of expressions and terms as integrated in knowledge structures, so that term functors, extendable to monads, become important instrumentations in applications. Categorical term constructions with applications to Goguen's category have been recently achieved (cf. Fuzzy Sets and Syst. 298, 128-157 (2016)). Information representation supported by such monads, and as constructed over monoidal closed categories, inherits many-valuedness in suitable ways also in implementations.
Bibliographische Angaben
- Autoren: Patrik Eklund , Javier Gutierrez Garcia , Ulrich Höhle , Jari Kortelainen
- 2019, Softcover reprint of the original 1st ed. 2018, XXI, 326 Seiten, Maße: 16 x 23,7 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3030076873
- ISBN-13: 9783030076870
Sprache:
Englisch
Pressezitat
"This monograph is a detailed and extensive investigation of the theory of quantales in different areas of mathematics. ... the book is self-contained, well-organized and well-written and is warmly recommended to read." (Ali Madanshekaf, zbMATH 1491.06001, 2022)
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